相关论文: Monolithic Hyper ROM FE$^2$ Method with Clustered …

Using Domain Decomposition (DD) algorithm on non--overlapping domains, we compare couplings of different discretisation models, such as Finite Element (FEM) and Reduced Order (ROM) models for separate subcomponents. In particular, we…

In this paper, we use the first-order virtual element method (VEM) to investigate the effect of shape quality of polyhedra in the estimation of the critical time step for explicit three-dimensional elastodynamic finite element (FE)…

Federated learning (FL) provides a distributed learning framework for multiple participants to collaborate learning without sharing raw data. In many practical FL scenarios, participants have heterogeneous resources due to disparities in…

Federated Learning (FL) enables collaborative training while keeping sensitive data on clients' devices, but local model updates can still leak private information. Hybrid Homomorphic Encryption (HHE) has recently been applied to FL to…

We present 2-D, 3-D, and spherical mesh generators for the Finite Element Method (FEM) using triangular and tetrahedral elements. The mesh nodes are treated as if they were linked by virtual springs that obey Hooke's law. Given the desired…

In this work we present a novel monolithic Finite Element Method (FEM) for the hydroelastic analysis of Very Large Floating Structures (VLFS) with arbitrary shapes that is stable, energy conserving and overcomes the need of an iterative…

Federated learning involves training machine learning models over devices or data silos, such as edge processors or data warehouses, while keeping the data local. Training in heterogeneous and potentially massive networks introduces bias…

This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the…

Federated learning (FL) has received a surge of interest in recent years thanks to its benefits in data privacy protection, efficient communication, and parallel data processing. Also, with appropriate algorithmic designs, one could achieve…

Federated learning (FL) enables on-device training over distributed networks consisting of a massive amount of modern smart devices, such as smartphones and IoT (Internet of Things) devices. However, the leading optimization algorithm in…

Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…

Multiple scale homogenization problems are reduced to single scale problems in higher dimension. It is shown that sparse tensor product Finite Element Methods (FEM) allow the numerical solution in complexity independent of the dimension and…

In this contribution, we derive a consistent variational formulation for computational homogenization methods and show that traditional FE2 and IGA2 approaches are special discretization and solution techniques of this most general…

This paper presents a high-order method for solving an interface problem for the Poisson equation on embedded meshes through a coupled finite element and integral equation approach. The method is capable of handling homogeneous or…

Coupled multiphysics simulations for high-dimensional, large-scale problems can be prohibitively expensive due to their computational demands. This article presents a novel framework integrating a deep operator network (DeepONet) with the…

These are the lecture notes of a short course on the homogenization method for topology optimization of structures, given by Gr\'egoire Allaire, during the "GSIS International Summer School 2018" at Tohoku University (Sendai, Japan). The…

The implementation of finite element methods (FEMs) for nonlocal models with a finite range of interaction poses challenges not faced in the partial differential equations (PDEs) setting. For example, one has to deal with weak forms…

Federated Learning (FL) revolutionizes collaborative machine learning among Internet of Things (IoT) devices by enabling them to train models collectively while preserving data privacy. FL algorithms fall into two primary categories:…

We present a class of methods for robust, personalized federated learning, called Fed+, that unifies many federated learning algorithms. The principal advantage of this class of methods is to better accommodate the real-world…

Federated Learning (FL) enables collaborative model training across distributed clients without sharing raw data, yet its performance deteriorates under statistical heterogeneity. Clustered Federated Learning addresses this challenge by…